A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discon- tinuous Galerkin (DG) formulation of the ... [more ▼]

A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discon- tinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms aris- ing from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the rein- statement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces. The main advantage of the method is that it avoids the need to propagate topo- logical changes in the mesh as cracks and fragments develop, which enables the indistinctive treatment of crack propagation across processor boundaries and, thus, the scalability in parallel computations. Another advantage of the method is that it preserves consistency and stability in the uncracked interfaces, thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches. A simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process. We also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries. [less ▲]

Objectives Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury. The reason for the prominence of TBI in these particular conflicts as opposed to ... [more ▼]

Objectives Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury. The reason for the prominence of TBI in these particular conflicts as opposed to others is unclear but may result from the increased survivability of blast due to improvements in body armor. In the military context blunt, ballistic and blast effects may all contribute to CNS injury, however blast in particular, has been suggested as a primary cause of military TBI. While blast effects on some biological tissues, such as the lung, are documented in term of injury thresholds, this is not the case for the CNS. We hypothesized that using bio-fidelic models, allowing for fluid-solid interaction and basic material properties available in the literature, that a blast wave would interact with CNS tissue and cause a possible concussive effect. Methods The blast shockwave on CNS tissue was modeled using a coupled computational fluid-solid dynamic simulation. The model included a complex finite element mesh of the head and intra-cranial contents. The effects of threshold and 50% lethal blast lung injury were compared with concussive impact injury using the full head model allowing know upper and lower bounds of tissue injury to be applied using pulmonary injury as the reference tissue. Results The effects of a 50% lethal dose blast lung injury (LD50) were comparable with concussive impact injury using the DVBIC – MIT full head model. Interpretation CNS blast concussive effects were found to be similar between impact mild TBI and the blast field associated with LD50 lung blast injury sustained without personal protective equipment. With the ubiquitous use of personal protective equipment this suggests that blast concussive effects may more readily occur in personnel due to enhanced survivability in the current conflicts. [less ▲]

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior [1]. When considering problems ... [more ▼]

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior [1]. When considering problems involving high-order derivatives, discontinuous Galerkin methods can also be seen as a means of enforcing higher-order continuity requirements in a weak manner [2,3]. Recently, the authors [4] have proposed a DG formulation for Kirchhoff-Love shell theory for which both the membrane and the bending response of the shell are considered. The proposed one-field formulation takes advantage of the weak enforcement in such a way that the displacements are the only discrete unknowns, while the C1 continuity is enforced weakly. The consistency, stability and rate of convergence of the numerical method are demonstrated for the case of a linear elastic material. In this work, this method is extended to shell problems involving finite displacements and finite deformations. [less ▲]

An explicit-dynamics spatially-discontinuous Galerkin (DG) formulation for non-linear solid dynamics is proposed and implemented for parallel computation. Discontinuous Galerkin methods have particular appeal in problems involving complex material response, e.g. non-local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes, and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi-discrete system of ordinary differential equations is integrated in time using a conventional second-order central-difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress-wave propagation and large plastic deformations. [less ▲]

Discontinuous Galerkin methods (DG) have particular appeal in problems involving high-order derivatives since they provide a means of weakly enforcing the continuity of the unknown-field derivatives. This ... [more ▼]

Discontinuous Galerkin methods (DG) have particular appeal in problems involving high-order derivatives since they provide a means of weakly enforcing the continuity of the unknown-field derivatives. This paper proposes a new discontinuous Galerkin method for Kirchhoff–Love shells considering only the membrane and bending response. The proposed one-field method utilizes the weak enforcement in such a way that the displacements are the only unknowns, while the rotation continuity is weakly enforced. This work presents the formulation of the new discontinuous Galerkin method for linear elastic shells, demonstrates the consistency and stability of the proposed framework, and establishes the method’s convergence rate. After a description of the formulation implementation into a finite-element code, these properties are demonstrated on numerical applications. [less ▲]

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the ... [more ▼]

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the consideration of compressibility effects in the fluid and their influence on the plate dynamics. The history of the pressure experienced by the plate is extracted from numerical simulations for arbitrary blast strengths and plate masses and used to infer the impulse per unit area transmitted to the plate. The numerical results complement some recent analytical solutions in the intermediate range of plate masses and arbitrary blast intensities where exact solutions are not available. The resulting beneficial effect of the fluid-structure interaction (FSI) in reducing transmitted impulse in the presence of compressibility effects is discussed. In particular, it is shown that in order to take advantage of the impulse reduction provided by the FSI effect, large plate displacements are required which, in effect, may limit the practical applicability of exploiting FSI effects in the design of blast-mitigating systems. (C) 2006 Elsevier Ltd. All rights reserved. [less ▲]

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and ... [more ▼]

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid–structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylor’s FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter. [less ▲]

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element ... [more ▼]

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element interfaces of the discretization. In order to ensure consistency and stability of the formulation, this approach requires the definition of a numerical flux and a stabilization term. Discontinuous Galerkin methods may also be formulated from a linear combination of the governing and compatibility equations weighted by suitable operators. A third approach based on a variational statement of a generalized energy functional has been proposed recently for finite elasticity. This alternative approach naturally leads to an expression of the numerical flux and the stabilization terms in the context of large deformation mechanics problems. This paper compares these three approaches and establishes the conditions under which identical formulations are obtained. [less ▲]

The impulse imparted by a blast wave to a freestanding solid plate is studied analytically and numerically focusing on the case in which nonlinear compressibility effects in the fluid are important, as is ... [more ▼]

The impulse imparted by a blast wave to a freestanding solid plate is studied analytically and numerically focusing on the case in which nonlinear compressibility effects in the fluid are important, as is the case for explosions in air. The analysis furnishes, in effect, an extension of Taylor's pioneering contribution to the understanding of the influence of fluid-structure interaction (FSI) on the blast loading of structures [The Scientific Papers of Sir Geoffrey Ingram Taylor, edited by G. K. Batchelor (Cambridge University Press, Cambridge, 1963), Vol. III, pp. 287-303] to the nonlinear range. The limiting cases of extremely heavy and extremely light plates are explored analytically for arbitrary blast intensity, from where it is concluded that a modified nondimensional parameter representing the mass of compressed fluid relative to the mass of the plate governs the FSI. The intermediate asymptotic FSI regime is studied using a numerical method based on a Lagrangian formulation of the Euler equations of compressible flow and conventional shock-capturing techniques. Based on the analytical and numerical results, an approximate formula describing the entire range of relevant FSI conditions is proposed. The main conclusion of this work is that nonlinear fluid compressibility further enhances the beneficial effects of FSI in reducing the impulse transmitted to the structure. More specifically, it is found that transmitted impulse reductions due to FSI when compared to those obtained ignoring FSI effects are more significant than in the acoustic limit. This result can be advantageously exploited in the design and optimization of structures with increased blast resistance. (c) 2006 American Institute of Physics. [less ▲]

in International Journal for Numerical Methods in Engineering (2006), 68(1), 6497

A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large ... [more ▼]

A discontinuous Galerkin formulation of the boundary value problem of finite-deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non-linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Copyright (c) 2006 John Wiley [less ▲]

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of ... [more ▼]

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid-structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body. [less ▲]

In this work, we demonstrate the feasibility of fully-Lagrangian finite element simulations of the mechanics of three-dimensional penetration environments. The key enabling component is a robust library ... [more ▼]

In this work, we demonstrate the feasibility of fully-Lagrangian finite element simulations of the mechanics of three-dimensional penetration environments. The key enabling component is a robust library informed with state-of-the-art algorithms for mesh healing and optimization, which is repeatedly used during the simulations to eliminate deformation-induced mesh distortion and to maintain the quality of the numerical solution. The computational strategy effectively avoids the need to resort to artifacts such as element deletion or conversion to meshless particles which have been proposed to eliminate the issue of mesh distortion. The effectiveness of the computational strategy is demonstrated in a simulation of deep oblique penetration of a spherical-nosed steel rod on an aluminum target. [less ▲]

A discontinuous Galerkin framework for large deformations of solids is established. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities ... [more ▼]

A discontinuous Galerkin framework for large deformations of solids is established. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. The focus of this paper is on the treatment of large elasto-plastic deformations. The method is shown to possess the required numerical properties: consistency in the non-linear range and linearized stability. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Further developments of the method will lead to applications where physical discontinuities must be modeled like fragmentation or failure. [less ▲]